Calculate Circle Perimeter: Given Radius = 4 Units

Circle Circumference with Given Radius

O is the center of the circle in the diagram.

What is its perimeter?

444OOO

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1

Understand the problem

O is the center of the circle in the diagram.

What is its perimeter?

444OOO

2

Step-by-step solution

To solve this problem, we will determine the circumference of the circle:

  • Step 1: Identify the radius, r r . From the diagram, the number 4 4 is provided, suggesting that r=4 r = 4 cm.
  • Step 2: Use the circumference formula for a circle: C=2πr C = 2\pi r .
  • Step 3: Substitute the radius into the formula: C=2π×4=8π C = 2\pi \times 4 = 8\pi cm.

Therefore, the circumference of the circle is 8π 8\pi cm. This aligns with choice 3 from the provided options.

The correct and verified circumference is 8π 8\pi cm.

3

Final Answer

8π 8\pi cm

Key Points to Remember

Essential concepts to master this topic
  • Formula: Circle circumference equals 2π times the radius
  • Technique: Substitute r = 4 into C = 2πr gives C = 8π
  • Check: Verify radius from center to edge measures 4 units ✓

Common Mistakes

Avoid these frequent errors
  • Using area formula instead of circumference formula
    Don't use A = πr² = π(4)² = 16π cm! This calculates the area inside the circle, not the distance around it. Always use C = 2πr for perimeter or circumference.

Practice Quiz

Test your knowledge with interactive questions

O is the center of the circle in the diagram.

What is its perimeter?

444OOO

FAQ

Everything you need to know about this question

What's the difference between perimeter and circumference?

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For circles, perimeter and circumference mean the same thing - the distance around the outside edge. Other shapes use 'perimeter' but circles specifically use 'circumference'.

Why do we use π in the formula?

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π (pi) represents the relationship between a circle's circumference and diameter. It's approximately 3.14, but we often leave answers in terms of π for exact values.

Should I calculate the decimal value of 8π?

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Keep your answer as 8π 8\pi unless the problem asks for a decimal approximation. The exact form is usually preferred in mathematics.

How do I know if the given measurement is radius or diameter?

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Look at the diagram carefully! The radius goes from center to edge, while diameter goes completely across through the center. In this problem, the line from O to the edge shows radius = 4.

What if I accidentally used the diameter formula?

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If you used C = πd (where d = diameter), you'd get C = 4π, which is half the correct answer. Remember: diameter = 2 × radius, so d = 8 when r = 4.

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